Properties

As a quotient

Proposition

If X∈PSh(Ringop)X \in PSh(Ring^{op}) is a smooth scheme then the canonical morphism

X→XdR
X \to X_{dR}

is an epimorphism (hence an epimorphism over each SpecRSpec R) and therefore in this case XdRX_{dR} is the quotient of the relation “being infinitesimally close” between points of XX: we have that XdRX_{dR} is the coequalizer